How close is this to the play?????

Fairly close (aside from obvious things such as realistic sets, etc.).

SPOILERS FOR BOTH FILM AND PLAY FOLLOW

One baffling difference is that most of the discussion of 'wit', and the importance of John Donne is gone. We get the set-up, when Bearing, as an undergrad, is told to rewrite her paper, and we get the final pay-off, when Jason explains it, but the meat of the issue, the discussions and illuminations of wit as a concept (and, especially, as a means of hiding from that which one fears) are mysteriously absent.

I watched the film first, years ago, and enjoyed it. It's well made, I confess. Then I bought and read the play. The play made me weep (in a public place, no less. Not something I enjoy doing). Further, at last I understand why the film is called 'Wit'. The DVD case claims that "Vivian Bearing is about to discover a fine line between life and death that can only be walked with wit." Bullfritters. The point of the piece is not the line between life and death, but "life and life everlasting." Vivian's extensive discussion and examination of wit in the poetry of John Donne is what allows us to see her more clearly. The film feels... hollow... to me now, having seen what it came from.

Truth be told, I could write more, but I trust I'm boring most of the people reading (plus I'd rather appreciate a break to think a little more extensively before spouting off any more).